HARMONIC ELECTROMOTIVE FORCE AND CURRENT. 55 



When the angle 6 is zero, e and i are said to be in phase 

 with each other. In this case e and i reach their maximum 

 values together, they pass through zero together, and so on. 



When the angle 6 is 90, e and i are said to be in quad- 

 rature with each other. In this case e is zero when i is at its 

 maximum value, and vice versa. 



When the angle 6 is 180, e and i are said to be in oppo- 

 sition. In this case e and i pass through zero together, but 

 when one is positive the other is negative. 



23. Composition and resolution of harmonic electromotive forces 

 and currents. It often happens that two or more harmonic elec- 

 tromotive forces (or currents) are added together. Thus, when 

 two alternators are connected in series their electromotive forces 

 are added, and when two alternators are connected in parallel 

 their currents are added. Again, it often happens that a given 

 harmonic electromotive force (or current) is divided into parts. 

 Thus, when two coils are connected in series between supply 

 mains, the supply voltage is divided between them, and when two 

 coils are connected in parallel between supply mains, the total 

 current is divided between them. The adding of harmonic elec- 

 tromotive forces (or currents) is 

 called composition, and the dividing 

 of a harmonic electromotive force 

 (or current) into parts is called 

 resolution. 



Composition. Consider two har- 



Fig. 45. 



monic electromotive forces e l and e 2 



of the same frequency. Let e l and e 2 be represented by the 

 lines Ej and E 2 in the clock diagram, Fig. 45. The sum e l + e 2 

 is a harmonic electromotive force of the same frequency as e l and 

 e v and this sum is represented by the line E, Fig. 45, which is 

 the geometric or vector sum of the lines ^ and E 2 . This is 

 evident when we consider that the projection, on any line, of the 

 diagonal of a parallelogram is equal to the sum of the projections 

 of the two adjacent sides of the parallelogram. 



